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Mirrors > Home > ILE Home > Th. List > albidv | GIF version |
Description: Formula-building rule for universal quantifier (deduction form). (Contributed by NM, 5-Aug-1993.) |
Ref | Expression |
---|---|
albidv.1 | ⊢ (𝜑 → (𝜓 ↔ 𝜒)) |
Ref | Expression |
---|---|
albidv | ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-17 1526 | . 2 ⊢ (𝜑 → ∀𝑥𝜑) | |
2 | albidv.1 | . 2 ⊢ (𝜑 → (𝜓 ↔ 𝜒)) | |
3 | 1, 2 | albidh 1480 | 1 ⊢ (𝜑 → (∀𝑥𝜓 ↔ ∀𝑥𝜒)) |
Colors of variables: wff set class |
Syntax hints: → wi 4 ↔ wb 105 ∀wal 1351 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-5 1447 ax-gen 1449 ax-17 1526 |
This theorem depends on definitions: df-bi 117 |
This theorem is referenced by: ax11v 1827 2albidv 1867 sbal1yz 2001 eujust 2028 euf 2031 mo23 2067 axext3 2160 bm1.1 2162 eqeq1 2184 cbvabw 2300 nfceqdf 2318 ralbidv2 2479 alexeq 2863 pm13.183 2875 eqeu 2907 mo2icl 2916 euind 2924 reuind 2942 cdeqal 2951 sbcal 3014 sbcalg 3015 sbcabel 3044 csbcow 3068 csbiebg 3099 ssconb 3268 reldisj 3474 sbcssg 3532 elint 3850 axsep2 4122 zfauscl 4123 bm1.3ii 4124 exmidel 4205 euotd 4254 freq1 4344 freq2 4346 eusv1 4452 ontr2exmid 4524 regexmid 4534 tfisi 4586 nnregexmid 4620 iota5 5198 sbcfung 5240 funimass4 5566 dffo3 5663 eufnfv 5747 dff13 5768 tfr1onlemsucfn 6340 tfr1onlemsucaccv 6341 tfr1onlembxssdm 6343 tfr1onlembfn 6344 tfrcllemsucfn 6353 tfrcllemsucaccv 6354 tfrcllembxssdm 6356 tfrcllembfn 6357 tfrcl 6364 frecabcl 6399 ssfiexmid 6875 domfiexmid 6877 diffitest 6886 findcard 6887 findcard2 6888 findcard2s 6889 fiintim 6927 fisseneq 6930 isomni 7133 isomnimap 7134 ismkv 7150 ismkvmap 7151 iswomni 7162 iswomnimap 7163 omniwomnimkv 7164 exmidfodomrlemr 7200 exmidfodomrlemrALT 7201 fz1sbc 10095 frecuzrdgtcl 10411 frecuzrdgfunlem 10418 zfz1iso 10820 istopg 13469 bdsep2 14608 bdsepnfALT 14611 bdzfauscl 14612 bdbm1.3ii 14613 bj-2inf 14660 bj-nn0sucALT 14700 sscoll2 14710 |
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